In general, it is desirable to be able to alter a graphical object in some simple and automatic way to give it a predetermined "style". For instance, taking letters of the alphabet, it is useful to give the letters a particular style such as Roman, Courier, etc. In order to do this, it is desirable to be able to transform an original rendering of a letter into a representation amenable to subsequent automatic machine modification which changes the letter into one having the required style by the application of some process so that all the letters look substantially consistent.
Likewise, in general it is desirable to give a predetermined characteristic to a graphical object so that all of the graphical objects come out rendered in a similar style.
Moreover, it is useful to be able to average shapes or combine two shapes by interpolation or extrapolation. Such transformations have not been easy in the past because one must analyze the shapes to identify important features. This is followed by an adhoc combination which in the past has been somewhat unsuccessful.